A162561 a(n) = ((4+sqrt(3))*(5+sqrt(3))^nv+v(4-sqrt(3))*(5-sqrt(3))^n)/2.

4, 23, 142, 914, 6016, 40052, 268168, 1800536, 12105664, 81444848, 548123872, 3689452064, 24835795456, 167190009152, 1125512591488, 7576945713536, 51008180122624, 343388995528448, 2311709992586752, 15562542024241664

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009

Keywords

• nonn

Comments

Third binomial transform of A077236. Fourth binomial transform of A162559. Fifth binomial transform of A162766.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10, -22).

Crossrefs

Cf. A077236, A162559, A162766.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009

Mathematica

LinearRecurrence[{10,-22},{4,23},30] (* Harvey P. Dale, Mar 27 2013 *)

Formula

a(n) = 10*a(n-1) - 22*a(n-2) for n > 2; a(0) = 4, a(1) = 23.

G.f.: (4-17*x)/(1-10*x+22*x^2).

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 14 2009